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The human sense of smell plays an important role in appetite and food intake, detecting environmental threats, social interactions, and memory processing. However, little is known about the neural circuity supporting its function. The olfactory tracts project from the olfactory bulb along the base of the frontal cortex, branching into several striae to meet diverse cortical regions. Historically, using diffusion magnetic resonance imaging (dMRI) to reconstruct the human olfactory tracts has been prevented by susceptibility and motion artifacts. Here, we used a dMRI method with readout segmentation of long variable echo-trains (RESOLVE) to minimize image distortions and characterize the human olfactory tracts in vivo . We collected high-resolution dMRI data from 25 healthy human participants (12 male and 13 female) and performed probabilistic tractography using constrained spherical deconvolution (CSD). At the individual subject level, we identified the lateral, medial, and intermediate striae with their respective cortical connections to the piriform cortex and amygdala (AMY), olfactory tubercle (OT), and anterior olfactory nucleus (AON). We combined individual results across subjects to create a normalized, probabilistic atlas of the olfactory tracts. We then investigated the relationship between olfactory perceptual scores and measures of white matter integrity, including mean diffusivity (MD). Importantly, we found that olfactory tract MD negatively correlated with odor discrimination performance. In summary, our results provide a detailed characterization of the connectivity of the human olfactory tracts and demonstrate an association between their structural integrity and olfactory perceptual function. SIGNIFICANCE STATEMENT This study provides the first detailed in vivo description of the cortical connectivity of the three olfactory tract striae in the human brain, using diffusion magnetic resonance imaging (dMRI). Additionally, we show that tract microstructure correlates with performance on an odor discrimination task, suggesting a link between the structural integrity of the olfactory tracts and odor perception. Lastly, we generated a normalized probabilistic atlas of the olfactory tracts that may be used in future research to study its integrity in health and disease.